Questions tagged [integer]
For challenges involving the manipulation of integers.
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Rudin-Shapiro sequence
The Rudin-Shapiro sequence is a sequence of \$1\$s and \$-1\$s defined as follows: \$r_n = (-1)^{u_n}\$, where \$u_n\$ is the number of occurrences of (possibly overlapping) \$11\$ in the binary ...
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Monotone sequence beatitude
Provided that the input is a monotone sequence of three or more integers:
Output -2 if the sequence strictly decreases. Example: [7,4,3,2]
Output -1 if the ...
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Add two natural numbers
Given two natural numbers (less than 100) as input print the sequence of intermediate results obtained when computing the sum of the two numbers using only the following operations1:
...
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Finding the power sandwich version 2
Introduction
This question is inspired by this great question.
Challenge
Given a number \$N>0\$, output the largest integer \$a^b\$ that is smaller or equal to \$N\$, and the smallest integer \$c^d\...
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Finding the power sandwich
Introduction
Finding the closest power to a number is a common enough problem. But what if you need both the next-highest and next-lowest power? In this challenge you must find the closest powers to a ...
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Help, I can't bloody well memorize this number!
The Brits aren't exactly known for being good at memorizing stuff. That's why scientists need newspaper articles to find those who are, and that's why it shouldn't be a surprise that they forget more ...
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The multiples are missing
Given a number \$n\$, you are to compute the sequence of positive numbers where for each number \$a\$, the \$n\$-times multiple \$n\cdot a\$ is missing.
Example
We always start with the sequence of ...
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Longest Consecutive Sequence
Description
Given a list of positive integers, write the shortest code to find the number count of the longest consecutive sequence of numbers within the list.
Input
A list of positive integers. You ...
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Sum of consecutive nth powers
Related.
Given a positive integer \$n\$, output all integers \$b\$ (such that \$1<b<n-1\$) where \$n\$ can be written as the sum of any number of consecutive powers of \$b\$.
Example:
Let's say \...
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Otteretto Classic game scoring method
Brief description of the game
In the game Otteretto Classic (which you can test directly in your browser; try it!) the player has to form palindromic sequences using adjacent cells on a square grid. ...
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Output the smallest increasing sequence where each term is coprime to preceding 3 terms
This sequence is defined as
Starts with 1, 2, 3
The next element of the sequence is the first number greater than the previous three that is co-prime with each of the previous 3 elements in the ...
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Is this a powerful number?
A powerful number is a positive integer \$n\$ such that for every prime \$p\$ that divides \$n\$, \$p^2\$ also divides \$n\$. Or equivalently, \$n\$ is powerful if and only if it can be written in the ...
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The number of solutions to Hertzsprung's Problem
Hertzprung's Problem (OEIS A002464) is the number of solutions to a variant of the Eight Queens Puzzle, where instead of placing \$n\$ queens, you place \$n\$ rook-king fairy pieces (can attack like ...
- 8,618
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Implement grambulation
Consider the following spiral of positive integers:
We now define grambulation as a binary operation \$\lozenge : \mathbb N \times \mathbb N \to \mathbb N\$, using this grid. Some example inputs and ...
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How many xor'ed waves?
In this challenge, you're given a list of overlapping waves. Each wave is a finite list with n truthy values, then n falsy ...
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Is it a Frog List?
Challenge:
A Frog List is defined by certain rules:
Each frog within a Frog List has an unique positive digit [1-9] as id (any 0...
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A Fine sequence with fine interpretations
The ubiquitous Catalan numbers \$C_n\$ count the number of Dyck paths, sequences of up-steps and down-steps of length \$2n\$ that start and end on a horizontal line and never go below said line. Many ...
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Determine the Octet(/Duplet/18-electron) Rule
Given an atomic number in the inclusive range [1,118], write the shortest program/function that outputs one of {2,8,18} if the ...
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Sum of Consecutive Squares
Your task
Given a integer input, \$ n \$ (such that \$ n > 1 \$), decide whether it can be written as the sum of (at least 2) consecutive square numbers.
Test cases
Truthy:
...
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Don't repeat yourself
In this challenge you will be tasked with implementing a sequence of natural numbers such that:
Each number appears a natural number of times
No two numbers appear the same number of times
No two ...
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Smallest Bit Rotation
For a given positive integer, try to find out the smallest possible rotation resulted by rotating it 0 or more bits.
For example, when the given number is 177, whose binary representation is \$...
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RADD decomposition of an integer
Introduction
The \$RADD(n)\$ operation is defined as the sum of \$n + [\$ the number whose decimal representation are the decimal digits of \$n\$ in reverse order \$]\$, see A004086. After reversal, ...
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4
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Find a matrix whose sliding sum is the input
Given a matrix like this:
1 1 3 -2
3 -4 1 -1
1 1 1 0
0 -1 0 0
By taking a 2×2 "sliding sum", where the sum of every 2×2 region of the matrix is ...
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Carryless factors
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition:
...
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Carry-less sum given a base b
Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
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Find number components with lowest distribution
Let us assume that we have number X.
Let us assume that we have positive integer "components" (C) of this ...
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Cryptic Multiplications
Given two non-negative integers e.g. 27, 96 their multiplication expression would be 27 x 96 = 2592.
If now each digits is ...
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Shifted auto-sum
Let’s take a positive integer such as 123. We define the shifted auto-sum of this integer as follows:
123 has 3 digits. We thus consider 3 copies of 123.
We stack ...
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14
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7
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Exponential transform of an integer sequence
The exponential generating function (e.g.f.) of a sequence \$a_n\$ is defined as the formal power series \$f(x) = \sum_{n=0}^{\infty} \frac{a_n}{n!} x^n\$.
When \$a_0 = 0\$, we can apply the ...
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How far from binary?
Given a decimal integer n as input, output the smallest (in terms of absolute value) decimal integer m such that the absolute ...
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Find the nth Fibonacci number, where n is the mth Fibonacci number
Introduction
If \$\newcommand{\fib}{\operatorname{fib}}\fib(x)\$ calculates the \$x\$th Fibonacci number, write a program that calculates \$\fib(\fib(m))\$ for any integer value of \$m \ge 0\$. (Of ...
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Spell out an integer... in NDos' way
Objective
Given a positive integer, spell it out in the conlang I made.
Specification
Let \$n\$ be the inputted integer. \$n\$ shall be spelled out in the following specification. The entire spelling ...
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Is it 1089-able?
\$ 1089 \$ is a very special number. To prove why, select any 3-digit number whose first and last digits differ by at least 2. Then, reverse the digits, and take the difference of these two numbers. ...
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The interstice of two binary numbers
Given two integers, compute the two numbers that come from the blending the bits of the binary numbers of equal length(same number of digits, a number with less digits has zeros added), one after the ...
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Randomly Rounding
Input a decimal number and round it to an integer, randomly rounding up or down with a probability based on its fractional part, so the expected value of the output equals to the input value.
If ...
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Double bit rotation to the right [closed]
Given a positive integer as input, output that integer, but with its bits rotated two times to the right. Also, think of the number as a donut of bits, eg. ...
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Line Islands in a Word Search
My third word search related challenge in a row. :)
Challenge:
Brief explanation of what a word search is:
In a word search you'll be given a grid of letters and a list of words. The idea is to cross ...
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3
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Find All Digitroot Cyclic Sequences With Length Greater Than One
Digital sum, DR, Digit root is the iterative process of summing digits of a number until you end up with a single digit root number: e.g. digit root of 12345 is 6 since 1 + 2 + 3 + 4 + 5 = 15 = 1+5. ...
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How-many-bonacci-like is this sequence?
Inspired by @emanresu A's Is it a fibonacci-like sequence? Make sure to upvote that challenge as well!
We say a sequence is Fibonacci-like, if, starting from the third term (\$1\$-indexed), each term ...
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3
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Coordinates for a Heronian tetrahedron
Did you know that Heronian Tetrahedra Are Lattice Tetrahedra? A Heronian tetrahedron is a tetrahedron where
the length of each edge is an integer,
the area of each face is an integer, and
the volume ...
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Sum of the first n elements of the sequence of 9's complement
Let's consider the following sequence:
$$9,8,7,6,5,4,3,2,1,0,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71...$$
This is the sequence of \$9\$'s complement of a number: that is, \$ a(x) = 10^...
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How many blocks make a "truncated square-pyramid garden"?
A truncated square-pyramid of height \$h\$ has \$h\$ square layers where each layer has a side \$1\$ greater than the one above it, apart from the top layer which is a square of blocks with a given ...
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Is it a fibonacci-like sequence?
The Fibonacci Sequence is a sequence of positive integers where the first two elements are 1 and the rest are the sum of the previous two. It begins \$1, 1, 2, 3, 5, 8, 13\$ and continues forever.
But ...
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Is given number a concat of two squares
Given a positive integer, determine if it can be represented as a concatenation of two square numbers. Concatenated numbers may not begin with 0 (except for 0). Any leading zeros in input should be ...
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Prime a*b+c of N
Given an integer \$N\$, print or return integers \$a\$, \$b\$, and \$c\$ that satisfy all of the following conditions, if such integers exist:
\$a \times b + c = N\$
\$a\$, \$b\$, and \$c\$ are all ...
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Represent any integer with an expression that uses no digit besides '4' [closed]
Fourward (Introduction)
I have an unhealthy obsession with the number 4. I love it so much, in fact, that seeing any other digit is frustrating to me. I therefour wish to create a 'Fourier ...
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Mirror an integer... in NDos' way
NDos' Numeral System
NDos' numeral system is a numeral system invented by me. It represents every nonnegative integer by a binary tree. Given a nonnegative integer \$n\$:
If \$n=0\$, it is ...
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Encode integers with some others
Input a non-empty array of positive (greater than 0) integers. Output another non-empty array of positive integers which encode the input array. Output array does not use any numbers used in the input ...
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Even sum subarrays
Given an array of integers, count the number of contiguous subarrays with an even sum. You may assume that the array is non-empty, and contains only non-negative integers.
This is code-golf, so the ...
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